## What does this infinite trigonometric identity have to do with probability?

Recently I came across this surprising trigonometric identity…

## A Devious Bet 2: Law of Large Numbers

You meet up with a slightly familiar mustached squid “man” He may or may not have bankrupted you infinitely times over in the past, but you’re over it. In fact he has a new deal for you! Every day he will modify your bank balance in one of two ways. With probability 0.6, your balance … Read more

## A Tale of Drunk Worms and Random Walks

Meet Larry the worm. Larry had a wonderful night drinking at a bar with his friends. Alas, Larry got a bit too drunk, so when he and his friends finished drinking, he went to walk (err, crawl) home, drunk. Larry and his friends live on a one dimensional road. As Larry is drunk, he walks … Read more

## A Devious Bet: The Borel-Cantelli Lemma

Suppose you are offered a bet as follows, by a totally not evil and totally not a squid monster disguised as a man casino owner. The bet will have (countably) infinitely many steps. In each you win or lose money, the only thing the totally not a squid monster tells you is that in each step, on average, you gain money. Furthermore, that average increases as the bet goes on. Do you take it?

## Why “almost surely” a math blog?

So why is this only “almost surely” a math blog? For technical reasons, it’s because maybe in the future some posts will not be about math but related subjects (or unrelated, perhaps in 2026 this blog will be about pistachios, who knows honestly). But the major reason I chose this title is as a reference … Read more

## How do we choose things? (at random)

Don’t you just hate it when you are asked to pick something “at random”? No? Well let me show you what I mean.